Abstract:

The invention relates to converting a first light signal (L1) into a
second light signal (L2) polarized according to a set of different states
of polarization, whereby the set of different polarization states is
represented by a corresponding set, of Stokes vectors in a Stokes space
representation, and wherein the end points of the set of Stokes vectors
span a geometric shape, wherein, in response to a desired geometric shape
with an arbitrary orientation in the Stokes space, a setting (C1, C2) of
at least two adjustable optical elements (22, 23) arranged in an optical
path between an optical input (201) and an optical output (202) is
determined such that, while varying the wavelength of the input signal
(L1) within a certain range, corresponding variations of the geometric
shape are below a desired value.

Claims:

1. A method of for converting a first light signal into a second light
signal polarized according to a set of different states of polarization,
wherein the set of different polarization states is represented by a
corresponding set of Stokes vectors in a Stokes space representation, and
wherein the end points of the set of Stokes vectors span a geometric
shape, comprising:determining, in response to a desired geometric shape
with an arbitrary orientation in the Stokes space, a setting of at least
two adjustable optical elements arranged in an optical path between an
optical input and an optical output such that, while varying the
wavelength of the input signal within a certain range, corresponding
variations of the geometric shape are below a desired value, andadjusting
the at least two optical elements of an arrangement of optical elements
according to the determined setting.

2. The method of claim 1, wherein the geometric shape is a line if the
number of states of polarization equals 2, a triangle if the number of
states of polarization equals 3 and a polyhedron if the number of states
of polarization is greater that 3.

3. The method of claim 1, further comprising:defining a merit function
representing the difference between the desired shape and the shape
resulting from a setting over the wavelength range,determining a
plurality of settings,selecting a setting out of the plurality of
settings that shows a minimum merit function.

4. The method of claim 3, wherein the plurality of settings is determined
by an iteration process by determining a first setting showing the
desired shape at one wavelength value, varying this setting and
determining the merit function for each variation until the merit
function is below a certain value.

5. The method of claim 2, wherein the merit function describes one of:a
mean variation of a sum of the angles between the Stokes vectors over the
wavelength range,a maximum variation of any angle between the Stokes
vectors over the wavelength range,a mean variation of the line length
over the wavelength range, if the number of states of polarization equals
two, or a mean variation of the polyhedron volume over the wavelength
range, if the number of states of polarization is greater than 3, anda
maximum variation of the line length over the wavelength range, if the
number of states of polarization equals two, or a maximum variation of
the polyhedron volume over the wavelength range, if the number of states
of polarization is greater than 3.

6. The method of claim 5, wherein the number of output states of
polarization equals 4, and wherein the settings are selected such that
the mean variation of the corresponding tetrahedron volume over a
wavelength range between 1250 nanometer and 1650 nanometer is below 1%.

7. The method of claim 1, wherein the at least two adjustable optical
components comprise a rotatable quarter-wave plate and a rotatable
half-wave plate, that are adjusted according to the settings by rotating
the wave plates.

8. The method of claim 7, wherein the at least two adjustable optical
components further comprise a rotatable polarizer, and wherein the
rotatable quarter-wave plate and a rotatable half-wave plate are adjusted
to the settings by rotating the wave plates in relation to the
polarization axis of the rotatable polarizer.

9. The method of claim 1, wherein the at least two adjustable optical
components comprise a plurality of wave plates each having an individual
tunable retardance, the wave plates being arranged at fixed relative
angles with respect to their optical axes, wherein their retardances are
adjusted according to the settings.

10. The method of claim 9, wherein the wave plates are opto-electrical
elements that change their retardances with respect to electric control
signals, and wherein the control signals are generated according to the
settings.

11. The method of claim 9, wherein the at least two adjustable optical
components further comprise a rotatable polarizer, and wherein the
retardances of the wave plates are adjusted according to the settings in
relation to the polarization axis of the rotatable polarizer.

12. The method of claim 3, wherein at least one of the following
parameters is received from a user interface:the wavelength range,the
number of states of polarization,the geometric shapethe merit function,
andthe desired value of the shape variation.

13. An polarization controller for converting a first light signal into a
second light signal polarized according to a set of different output
states of polarization, wherein the set of different polarization states
is represented by a corresponding set of Stokes vectors in a Stokes space
representation, and the end points of the set of Stokes vectors span a
geometric shape, comprising:an optical input adapted for receiving the
first light signal having an input state of polarization,an optical
output adapted for emitting the second light signal having one of the
states of the set of different output states of polarization,an
arrangement of optical elements positioned in an optical path between the
optical input and the optical output, whereof at least two of the optical
elements are adjustable, anda control unit adapted to determine, in
response to a desired geometric shape with an arbitrary orientation in
the Stokes space, settings of the at least two adjustable optical
elements such that, while varying the wavelength of the input signal
within a certain range, corresponding variations of the geometric shape
are below a desired value.

14. A software program or product, embodied on a computer readable medium,
for controlling or executing the method of claim 1, when run on a data
processing system of a polarization controller.

Description:

[0002]For determining optical properties of an optical device under test
(DUT), a set of probing signals with defined polarization states is
commonly used. Such polarization states might be generated by means of a
polarization controller, such as the Agilent 8169A Polarization
Controller. This polarization controller allows for providing probe
signals at precisely synthesized states of polarization. The response
signals returning from the DUT allows for determining optical properties
of a DUT. Information about the Agilent 8169A Polarization Controller can
be drawn from the technical specifications available at Product or
Service Web Pages of Agilent Technologies Inc. or from the patent
application US 2004/0067062 A1 of the same applicant.

[0003]Different methods are known for determining optical properties the
DUT. According to the so-called Mueller Method, probing signals at four
precisely synthesized, e.g. tetragonal, states of polarization are
provided to the DUT and the power of the optical signals returning from
the DUT are detected. From the known input states of polarization and the
measured signal powers, the elements of so-called Mueller are determined.
From elements of this Matrix, optical properties of the DUT, e.g. the
minimum and maximum insertion loss, polarization dependent loss (PDL),
the group delay (GD) or the differential group delay (DGD) can be
derived.

[0004]Alternatively the so called Jones matrix method is known, wherein
the optical properties are derived by measuring the output states of
polarization of the signals returning from the DUT for at least two,
preferably orthogonal states of polarization in a further alternative a
variant of the Mueller method might be applied by applying a set of six,
preferably orthogonal states of polarization.

DISCLOSURE

[0005]It is an object of the invention to provide an improved generating
of optical signals with defined polarization states. The object is solved
by the independent claims. Further embodiments are shown by the dependent
claims.

[0006]Each state of polarization (SOP) of the polarization controller can
be regarded as a vector in a Stokes space. The endpoints of these
vectors, further also referred to as SOP system, span a geometric shape.
Depending on the number of endpoints, the geometric shape is a line (two
endpoints), a triangle (3 endpoints) or a polyhedron (more that three
endpoints).

[0007]For the important case of four states of polarization used for the
above-mentioned Mueller Method, the polyhedron is a tetrahedron
comprising four triangular faces that are not necessarily equal. A
regular tetrahedron is a tetrahedron of four equal triangular faces.

[0008]One problem of polarisation controller used for a wide range of
wavelengths is that while changing the wavelength of an input signal of
the polarisation controller, the SOP system will not remain constant.
Depending on the settings of the polarization controller, the changes of
the SOP system over a regarded wavelength range may be significantly
high.

[0009]The invention is based on the insight that the absolute change of an
SOP system within the Stokes space is often not of any significance, as
long as the geometric shape does not significantly change, i.e.
variations of the relative orientations of the Stokes vectors to each
other do not significantly change. To the contrary, significant changes
of the geometric shape, e.g. a relative volume change of a regular
tetrahedron spanned by four tetragonal SOP's of more than +/-5%, are
often unacceptable.

[0010]According to embodiments of the inventions, in response to a desired
geometric shape with an arbitrary orientation in the Stokes space, a
setting of adjustable optical elements, arranged in an optical path
between an optical input and an optical output of a polarization
controller, are determined such that, while varying the wavelength of an
input signal within a certain range, corresponding variations of the
shape of the polyhedron are kept small. In other words, such variations
shall mainly results in a rotation of the shape.

[0011]Therewith the invention allows keeping the settings fix when
performing wavelength sweeps without varying the respective settings,
e.g. the angular position of a quarter wave plate and a half wave plate
in dependence on the wavelength of the incident light, or without
performing additional measurements of the output SOP's at different
wavelengths.

[0012]In an embodiment, a merit function representing the difference
between the desired shape and the shape resulting from a setting over the
wavelength range is defined. Generally, a merit function is a function
that measures the agreement between data and the fitting model for a
particular choice of the parameters. By convention, the merit function is
small when the agreement is good. Therefore, a plurality of settings is
determined and the merit functions of the different settings are
determined. Then, a setting out of the plurality of settings is selected
that shows the minimum merit function.

[0013]In an alternative embodiment, the plurality of settings is
determined by an iteration process. This process might start with a first
setting showing the desired polyhedral at one wavelength value and
stepwise varying this setting. For each setting, the merit function is
determined. If the merit function is below a defined value, the
corresponding setting is selected. Otherwise the iterative process is
continued with further variations of the settings.

[0014]In further embodiments, the merit function represents a mean
variation of a sum of the angles between the Stokes vectors over the
wavelength range, a maximum variation of any angle between the Stokes
vectors over the wavelength range, a mean variation of the line length
over the wavelength range, if the number of states of polarization equals
two, or a mean variation of the polyhedron volume over the wavelength
range, if the number of states of polarization is greater than 3, or a
maximum variation of the line length over the wavelength range, if the
number of states of polarization equals two, or a maximum variation of
the polyhedron volume over the wavelength range, if the number of states
of polarization is greater than 3. It is apparent the merit functions
listed above only serve as examples.

[0015]In further embodiment, the at least two adjustable optical
components comprise a rotatable quarter-wave plate and a rotatable
half-wave plate, that are adjusted according to the settings by rotating
the wave plates.

[0016]In a further embodiment, the adjustable optical components comprise
a plurality of wave plates, each of the wave plates having an individual
tunable retardance. The wave plates are arranged with fixed relative
angles with respect to their optical axes. The wave plates might be
arranged to be rotated together or to be absolutely fixed. In order to
control the polarization, the retardances of the wave plates are adjusted
according to the settings (C1, C2).

[0018]In a further embodiment, three wave plates of variable retardance
optically connected in series are comprised, wherein in idle or nominal
state, the first wave plate and the third wave plate show half wave plate
characteristics and the second wave in-between plate shows quarter wave
plate characteristics.

[0019]With properly chosen wave plate settings, retardance errors of the
wave plates over the wavelength ate converted into a slow rotation of the
complete SOP-system, thus reducing the change of the shape spanned by the
SOP vectors over wavelength, and thus enabling measurements over wide
wavelength ranges with minimized errors As shape changes affect noise and
sensitivity to measurement errors like detector PDL, the invention allows
for minimizing such errors.

[0020]In a further embodiment, a rotatable polarizer is comprised, so that
the rotatable quarter-wave plate and a rotatable half-wave plate might be
adjusted to the settings by rotating the wave plates in relation to the
polarization axis of the rotatable polarizer.

[0021]In a further embodiment selected ones of the following parameters
might be entered by a user or might be selected from a set of proposed
values by a user. Examples for such parameters are as follows: the
wavelength range, the number of states of polarization, the geometric
shape the merit function, and the desired value of the shape variation.

[0022]In a further embodiment, the invention allows for reducing the
impact of retardance errors to measurement results even at single
wavelength measurements.

[0023]Embodiments of the invention can be partly or entirely embodied or
supported by one or more suitable software programs, which can be stored
on or otherwise provided by any kind of data carrier, and which might be
executed in or by any suitable data processing unit.

BRIEF DESCRIPTION OF DRAWINGS

[0024]Other objects and many of the attendant advantages of embodiments of
the present invention will be readily appreciated and become better
understood by reference to the following more detailed description of
embodiments in connection with the accompanied drawings. Features that
are substantially or functionally equal or similar will be referred to by
the same reference signs.

[0025]FIG. 1 shows a block diagram of a measurement setup for determining
optical properties of a DUT, comprising a polarization controller
according to the invention,

[0026]FIG. 2 shows a representation of a set of four exemplary tetragonal
polarization states in a Poincare sphere,

[0030]FIG. 1 shows a measurement setup for determining optical properties
of an optical device under test (DUT) 3. A light source 1, preferably a
tunable laser source, generates a first light signal L1. Said first light
signal L1 is provided to a polarization controller 2, which generates a
second light signal or probe signal L2 to be provided to the DUT 3,
thereby transforming the input state into one of a set of different
output states of polarization, e.g. of a set of four tetragonal
polarization states. In response to the probe signal 2, the DUT emits a
response signal L3. The response signal L3 might be a signal received
through transmitting the through the DUT 3 or a reflected from the DUT 3.
The DUT response signal L3 is provided to a detector 4, which determines
the signal power of the response signal L3. For each one of the set of
polarization states of the light signal L1, a corresponding signal power
of the response signal L3 is obtained.

[0031]The relationship between the various polarization states on the one
hand and the corresponding set of signal powers on the other hand allows
getting a picture of the DUT's optical behavior. In case a tunable laser
source is used as a light source 1, wavelength sweeps of the light signal
2 over a certain wavelength range might be performed. This allows
recording the DUT's optical properties over the certain wavelength range.

[0032]The polarization controller 2 comprises a set of optical elements
21, 22, 23 that are positioned in series within the optical of the light
signals L1 and L2. The optical elements are individually adjusted to
create a desired polarization change between the input SOP of the first
signal L1 to an output SOP of the second signal L2. In an embodiment, the
polarization controller 2 comprises a quarter-wave plate 22 and a
half-wave plate 23. These plates 22, 23 are also known as retardation
plates or wave plates.

[0033]The quarter-wave plate 22 and the half-wave plate 23 are realized as
being rotatable around a propagation axis of the incident light beam. The
plates are each rotated by a determined angle to achieve a desired output
state of polarization state. The rotation positions, e.g. relative to a
polarization axis of the first light signal L1, can be denoted by angles
α and β.

[0034]Retardation plates are optical elements with two principal axes, one
slow axis and one fast axis that resolve an incident polarized beam into
two mutually perpendicular polarized beams. Their operation is based on
birefringent linear effect, which is the difference in the refractive
indices for the beams with parallel and normal polarization towards the
optical axis of the crystalline quartz material being within the wave
plate plane. The emerging beam recombines to form a particular single
polarized beam.

[0035]The thickness of a half wave plate is such that the phase difference
is one half of the wavelength (zero-order wave plate) or defined
multiples of one half of the wavelength (multi-order wave plates). A
linearly polarized beam incident on a half wave plate emerges as a
linearly polarized beam but rotates such that its angle to the optical
axis is twice that of the incident beam. Therefore, half wave plates can
be used as continuously adjustable polarization rotators.

[0036]The thickness of the quarter wave plate is such that the phase
difference is one quarter of the wavelength (zero-order wave plate) or
defined multiples of one quarter of the wavelength (multi-order wave
plates). If the angle q between the electric field vector of an incident
linearly polarized beam and the principal plane of the quarter wave plate
is 45, the emergent beam is circularly polarized.

[0037]The above-described wave plates, especially the multi-order wave
plates, are by their physical nature strongly dependent on the
wavelength. Therefore so-called achromatic wave plates are available
showing a reduced dependency from the wavelength in a certain range. Such
achromatic wave plates might comprise double retardation plates of two
different birefringent crystals. However, such wave plates are expensive
and only how a reduced wavelength dependency, that might not be
sufficient for high accuracy measurements.

[0038]The polarization controller 2 might further comprise an input
polarizer 21 so that the retardation plates 22 and 23 are set relative to
the input polarizer 21. The input polarizer might me additionally
rotatable.

[0039]The polarization controller 2 further comprises a control unit 24
for determining the positions of the optical elements 21, 22, 23.
Therefore the control unit 24 calculates control values C1-C2 to be
provided to the optical elements to be set to the desired rotation
angles.

[0040]The optical behavior of a DUT can be described by means of a Mueller
matrix M, which is a 4×4 real matrix. Any equivalent matrix that
represents the DUT's optical properties, e.g. a Jones matrix, can be used
as well. The light signal incident upon the DUT can be described by a
Stokes vectorSin=(S0in,S1in,S2in,S3in), and the
response signal obtained from the DUT can be described by a Stokes
vectorSout=(S0out,S1out,S2out,S3out). A Stokes
vector S=(S0,S1,S2,S3) completely describes the power and polarization
state of an optical wave, whereby S0 denotes the total intensity, S1
indicates the degree of linear horizontal (S1>0) or vertical
polarization (S1<0), S2 indicates the degree of linear +45°
(S2>0) or -45° (S2<0) polarization, and S3 corresponds to
the degree of right-hand circular (S3>0) or left-hand circular
(S3<0) polarization.

[0041]The interaction of an incident polarized wave characterized by the
Stokes vector Sin with the DUT can be expressed by means of the
matrix equation:

Sout=MSin

[0042]This matrix equation represents four linear equations, but only the
first one of said four equations is interesting for practical purposes.
According to said first equation, the signal power S0out of a DUT
response signal can be expressed as follows:

S0out=m11S0in+m12S1in+m13S2in+m14S-
in

[0043]In this equation, the Mueller matrix elements m1k, with k=1, 2,
3, 4, correspond to the first row of the Mueller matrix M. In order to
determine the elements m11, m12, m13, m14 of the
Mueller matrix, four different well-defined states of polarization
Sin,1,Sin,2,Sin,3,Sin,4 are consecutively applied to
the device under test, and the signal powers of the corresponding DUT
response signals are measured.

[0044]Once the Mueller matrix elements m11, m12, m13,
m14 are known, a multitude of optical properties of the DUT can be
derived there from. For example, the Mueller matrix element m11
indicates the "average loss" of the DUT. The minimum transmission
Tmin and the maximum transmission Tmax can be obtained as

Tmin=m11- {square root over
(m122+m132+m142)}

Tmax=m11+ {square root over
(m122+m132+m142)}

[0045]From these transmission extrema, the polarization dependent loss
(PDL) can be determined as

PDL dB = 10 log ( T max T min ) ##EQU00001##

[0046]As soon as the first row of the Mueller matrix is known, any other
optical property can be derived as well.

[0047]FIG. 2 shows a representation of a set of four exemplary tetragonal
polarization states in a Poincare sphere. The endpoints of the four
Stokes vectors Sa, Sb, Sc, Sd define a regular
tetrahedron, which is the most symmetric arrangement of four points on a
sphere. The principal axis 12 of the DUT is shown, which is defined by
the state of maximum transition 13 and the state of minimum transition
14. The principal axis 12 is arbitrarily oriented relative to the four
states of polarization Sa, Sb, Sc, Sd. In the example
shown in FIG. 2, the four states of polarization are defined as follows:

[0048]FIGS. 3a and 3b show angle of angles between stokes vectors of an
exemplary tetrahedral SOP system and a corresponding relative volume
variation over a wavelength range between 1250 nanometer and 1650
nanometer for a following exemplary pairs of settings of rotation angle
α of the quarter wave plate 22 and rotation angle β of the
half wave plate 23:

α={6.6,3.0,18.9,-54.45}

β={-1.0,-64.9,63.15,75.5}

[0049]FIG. 3a shows a diagram with the six relative angles α12,
α13, α14, α23, α24, α34 between the four
Stokes vectors Sa, Sb, Sc and Sd.

[0050]As can be seen from the diagram, the average variation of the angles
is below 10 degree and even the maximum change of any angle (here: al 2)
is below 20 degree.

[0051]FIG. 3b shows a diagram of a Volume of the tetrahedral compared to a
nominal Volume. As can be seen from this drawing, the relative Volume
change is in the range of 1 percent over the whole wavelength range. This
change is far smaller in selected smaller wavelength ranges.